Theory of Third-Order Differential Equations - Hardcover

Críticas

“This monograph is devoted to the qualitative behavior of solutions (oscillation, non-oscillation, stability, asymptotic behaviors, etc.) of various ordinary differential equations of third order with and without delay. It is suitable for those mathematicians and of other sciences dealing with mathematics and engineering. ... In summary, this monography is useful for researches investigating the qualitative behavior of solutions of ordinary differential equations of third order.” (Cemil Tunç, zbMATH 1308.34002, 2015)

“This is a comprehensive monograph on third-order differential equations, spanning more than 500 pages and collecting recent results on qualitative behavior of solutions of these equations. ... the book may serve as a basis for understanding the oscillatory and asymptotic theory of third-order differential equations, offering a comprehensive account of today’s knowledge in the field and a rich source of references for specialists.” (Zuzana Došlá, Mathematical Reviews, November, 2014)

Reseña del editor

This book discusses the theory of third-order differential equations. Most of the results are derived from the results obtained for third-order linear homogeneous differential equations with constant coefficients. M. Gregus, in his book written in 1987, only deals with third-order linear differential equations. These findings are old, and new techniques have since been developed and new results obtained.

Chapter 1 introduces the results for oscillation and non-oscillation of solutions of third-order linear differential equations with constant coefficients, and a brief introduction to delay differential equations is given. The oscillation and asymptotic behavior of non-oscillatory solutions of homogeneous third-order linear differential equations with variable coefficients are discussed in Ch. 2. The results are extended to third-order linear non-homogeneous equations in Ch. 3, while Ch. 4 explains the oscillation and non-oscillation results for homogeneous third-order nonlinear differential equations. Chapter 5 deals with the z-type oscillation and non-oscillation of third-order nonlinear and non-homogeneous differential equations. Chapter 6 is devoted to the study of third-order delay differential equations. Chapter 7 explains the stability of solutions of third-order equations. Some knowledge of differential equations, analysis and algebra is desirable, but not essential, in order to study the topic.